Waves not showing at final render
Dynamic Paint is the answer, but it seems to be a little tricky here. But this works...
For your &quot;mirror', it should be a canvas of type waves.

The object should be fairly subdivided, so I used a Subdivision Surface above the Dynamic Paint in the stack.
Here is the modifier stack for our mirror:

Next, I used an icosphere for the Brush in this example.
The settings are at the default.


Finally, the brush (icosphere) is animated from one point to another to contact the canvas, scale is also animated to increase on contact. Here, we have a cube parented to the icosphere, something like this may be an option in your scene. Constraints such as Copy Transform, and Limit Scale may be useful for that purpose. This is the result: